Geodesic
On Mealy--Moore coding and images of Markov measures
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 1, pp. 105-135

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We study the images of the Markov measures under transformations generated by the Mealy automata. We find conditions under which the image measure is absolutely continuous or singular relative to the Markov measure. Also, we determine statistical properties of the image of a generic sequence. 
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R. Grigorchuk; R. Kogan; Ya. Vorobets. On Mealy--Moore coding and images of Markov measures. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 1, pp. 105-135. http://geodesic.mathdoc.fr/item/MMO_2021_82_1_a5/